In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms of a vector space) in such a way that the Lie bracket is given by the commutator.
The notion is closely related to that of a representation of a Lie group. Roughly speaking, the representations of Lie algebras are the differentiated form of representations of Lie groups, while the representations of the universal cover of a Lie group are the integrated form of the representations of its Lie algebra.
Read more about Lie Algebra Representation: Formal Definition, Infinitesimal Lie Group Representations, Properties, Representation On An Algebra
Famous quotes containing the words lie and/or algebra:
“All morality depends upon our sentiments; and when any action or quality of the mind pleases us after a certain manner we say it is virtuous; and when the neglect or nonperformance of it displeases us after a like manner, we say that we lie under an obligation to perform it.”
—David Hume (1711–1776)
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (1883–1955)